19. On the Deaths of Massive Stars

19 On the Deaths of Massive Stars

19.1 Useful References

• Prialnik, 2nd ed., Ch. 10

• Kippenhahn, Weiger, and Weiss, 2nd ed., Chap. 36

• Hansen, Kawaler, and Trimble, Secs. 2.6–2.8

19.2 Introduction

Stars with initial masses � 6M� will end their days as the degenerate whitedwarfs we came to know and love in Sec. 16. But more massive stars will suffernew and different evolution and final fates: in core-collapse supernovae.

The most famous such event in living memory was the infamous SN1987A,which occurred “right next door” in the Large Magellanic Cloud (just 50 kpcaway) in Feb. 1987. It was the first core-collapse supernova whose progenitorstar could be uniquely identified and characterized (from archival data) – itwas Sanduleak, a 14,000 K supergiant with mass of ≈ 18M� (probably rathermore at formation) and pre-collapse luminosity of ≈ 105L�. Its light curve isshown in Fig. 41.

19.3 Eddington Luminosity

One interesting point is that stars with initial masses � 5M� never ascend agiant branch. Instead they start much hotter and evolve to the right on the H-R diagram at roughly constant luminosity. This constant L is because the starsare emitting at roughly the maximum permissible luminosity, the so-calledEddington Luminosity.

To derive this maximum luminosity, LEdd, we need three ingredients: hy-drostatic equilibrium, radiation energy transport, and radiation pressure. Re-call that for a stable star in hydrostatic equilibrium, Eq. 192 says that its pres-sure gradient must be

dPdr

= ρ(r)g(r).

For intense radiation fields (i.e., energy transported by radiation not convec-tion) the thermal profile (Eq. 235) is

dTdr

= − 3ρκL(r)64πσSBT3r2 .

And finally, radiation pressure is given by (Eq. 258)

Prad =13

�4c

�σT4.

An object (whether star or accreting supermassive black hole) has its maxi-mum luminosity, LEdd, when the radiation pressure gradient just balances the

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19.4. Core Collapse and Neutron Degeneracy Pressure

hydrostatic gradient. Taking the derivative of Prad, we have

dPraddr

=16σ

3cT3 dT

dr

(451)

=16σ

3cT3

�− 3ρκL(r)

64πσSBT3r2 .�(452)

= − ρκL4cπr2

(453)

(454)

This last expression must just equal −ρg; setting g = GM/R2 we then have

LEdd =4πcGM

κ

(455)

≈ (3.5 × 104L�)�

MM�

�(456)

(457)

for an approximate value of κ ≈ 0.34 cm2 g−1.

19.4 Core Collapse and Neutron Degeneracy Pressure

As we saw in Fig. 40, the most massive stars will undergo successive layersof shell burning, each shorter-lived than the last. Eventually the core is com-posed of 56Fe (up to around 1.5M� for M∗ � 20M�), which is inert from afusion standpoint (just like every other inert core which preceded it duringthe evolution process).

Two factors cause the core to collapse. First, as we saw in Sec. 17.6, photo-disintegration of the Fe nuclei will set in once Tc � 3 × 109 K; this absorbs thephotons that were previously providing radiation pressure support. Second,electron degeneracy pressure will also eventually drop: the degenerate elec-trons are forced into ever-higher energy states until they can initiate inversebeta decay:

(458) e− + p → n + ν̄e.

The star is undergoing neutronization and emitting copious neutrinos. Thenumber of free electrons declines and so electron degeneracy pressure willdecrease.

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19. On the Deaths of Massive Stars

Core collapse

The core is collapsing. What, if anything, can halt the collapse?The answer is neutron degeneracy pressure. This is the same phenomenon

we first encountered in Sec. 16.3, but provided by the neutrons instead. Thephysics is true but the names have been changed to protect the innocent; allrelevant scales are all now mn/me ≈ 1800× smaller. We can estimate the sizeof a neutron star using the same arguments in Eq. 381:

(459) Nnλ3D ≈ R3

where the de Broglie wavelength of the relativistic neutrons is

(460) λD ≈ hmnc

≈ 1.3 × 10−15 m

and so

(461) Nn ≈ 1.5M�/mn ≈ 1.8 × 1057.

That’s a lot of neutrons! At that scale, the expected size is roughly

(462) RNS ≈ hmnc

N1/3 ≈ 12 km.

Contrast this with the size of a white dwarf (or of the initial degeneratecore), which is roughly 1800× larger (but actually a bit less, because the com-position is more complicated) – RWD ≈ R⊕ = 6400 km.

Thus once hydrostatic support is lost, the core collapses from a size of≈ R⊕ to ≈ 12 km in a free-fall timescale:

(463) τf f ∼ (Gρ)−1/2

which is � 3 s for the initial core, and a much shorter timescale by the end ofthe collapse.

Energy Release

The total gravitational energy liberated by this collapse is considerable:

ΔE ≈ 35

GM2

R f− 3

5GM2

Ri

(464)

≈ 35

GM2

R f

(465)

≈ 3 × 1053 erg = 3 × 1046 J(466)

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19.4. Core Collapse and Neutron Degeneracy Pressure

which is all released in of order a second.

Contrast this with the Solar luminosity, L� ≈ 4 × 1033 erg. This collapse(which has now become a core-collapse supernova) is over 1020× more lumi-nous than the present-day Sun. Even over the Sun’s entire lifetime of 1010 yr,it will emit ∼ 1051 erg. So in a few seconds, a core-collapse supernova releases100× more energy than the Sun will in its entire life.

Where does all that energy go?

Photodisintegration captures a bit of it. The destruction of 56Fe releasesabout 125 MeV per nucleus, or about ∼2 MeV per nucleon. There are roughlyNFe ≈ 1.4M�/56mp ≈ 3× 1055 Fe nuclei in the core at collapse, so this absorbsroughly 6 × 1051 erg, or roughly 6% of the total.

Observed outflows from supernovae have velocities of vej ∼ 104 km s−1,far above the necessary escape speed. With an envelope mass of order 10M�,these will carry away roughly energy away,

K =12

Menvv2ej

(467)

≈ 12(10 × 2 × 1033)(109)2

(468)

≈ 1051(469)

or roughly 1% of the total.

Ejection of the envelope only uses a smidgen, despite the considerableenvelope mass. Even if all that mass were at the core radius, we would stillhave

ΔU ≈ GMenv Mc

Rc

(470)

≈ (2/3 × 10−7)(10 × 2 × 1033)(2 × 1033)

7 × 1010

(471)

≈ 4 × 1051 erg(472)

so as much as 4% (and probably a bit less, since some mass started at largerradii).

Supernovae are almost always discovered via their optical/infrared emis-sion, which rises rapidly (see Fig. 41 but persists for weeks to months. Veryroughly, assuming one year of emission at a typical supernova luminosity of

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19. On the Deaths of Massive Stars

3 × 1010L� gives

LSN ≈ (3 × 1010)(4 × 1033)(3 × 107)

(473)

≈ 4 × 1051 erg(474)

which is again just a few percent of the total energy release.

Neutrino Luminosity

Most of the energy actually goes into neutrinos. Despite their weak interactionswith baryonic matter, these fleeting leptons are created in sufficient numbers(and the collapsing star achieves such high densities) that enough neutrinoopacity results to help eject the envelope. In 1987, ∼20 electron neutrinos wereobserved from SN1987A.

During neutronization, the entire Fe core is converted into a neutron core— the precursor to a neutron star — via inverse beta decay. The total number

Days since shock breakout

0

1.0

Rela

tive F

lux

Figure 41: Supernova light curves at visible wavelengths. Left: Early phase ofa supernova outburst captured by the Kepler space telescope (Garnavich etal. 2016). Right: Multi-year light curve of SN1987A (https://www.eso.org/public/images/eso0708c/).

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19.5. Supernova Nucleosynthesis

of neutrinos produced will be roughly

Nν = Np

(475)

≈ 1.5M�2mp

(476)

≈ (2 × 1033)(6 × 1023)

(477)

≈ 1057(478)

The neutrinos produced are highly relativistic, and despite their minisculemasses (� 0.1 eV) they have typical energies of ∼30 MeV. Thus they carryaway � 5 × 1052 erg, and so transport the bulk of the energy liberated by thecore’s collapse. A wee bit of the copious neutrino flux couples to the densestellar material; this is still an active area of SN research.

19.5 Supernova Nucleosynthesis

Although core fusion has ceased in our dying massive star, nucleosynthesishas not. Given the colossal neutron fluxes present in these final moments,new nuclear pathways open up that were unavailable before; recall that theneutron has no charge, and so can proceed without needing to overcome thestrong Coulomb repulsion that hindered us in Sec. 14.3.

Figure 42: Nucleosynthesis via the s-process and r-process. Only a subset ofthe possible nuclei (and only the stable isotopes) are shown. Letters indicatewhich process can form which isotopes. From http://www.astro.sunysb.

edu/lattimer/PHY521/nucleo.pdf.

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19. On the Deaths of Massive Stars

As long as stable isotopes are formed, neutron capture can lead to a con-tinuous path of isotopes:

AZ X + n →A+1

Z X(479)

A+1Z X + n →A+2

Z X(480)

and so forth. But sooner or later an unstable isotope will be formed. Whathappens next depends on the relative timescales of neutron capture and betadecay. Fig. 43 depicts the two possible paths; so long as neutron capturesoccur, the nucleosynthesis track moves steadily to the right.

If neutron captures are relatively infrequent, then the isotope will beta-decay before another neutron can be jammed into the nucleus. This is thes-process (“s” for the slow neutron capture rate). This occurs, for example, inthe cores of asymptotic giant branch (AGB) stars, where the H-shell burningprovides the neutrons and large-scale instabilities lead to dredge-up. The betadecay follows its usual course:

(481) A+NZ X →A+N

Z+1 Y + e− + ν̄

and it could either be followed by more beta decays if the daughter nucleusA+NZ+1 Y is unstable

(482) A+NZ+1 Y →A+N

Z+2 Ω + e− + ν̄

(thus moving one step up and one to the left in Fig. 43) or by resuming thetrain of neutron captures if A+N

Z+1 Y is stable

(483) A+NZ+1 Y + n →A+N+1

Z+1 Y

(and thus moving steadily to the right again in Fig. 43). One of the moreunusual s-process products is Technetium, which has no stable isotopes but isstill seen in stellar spectra of evolved, late-type stars.

Alternatively, in a high-neutron-flux environment (such as our collapsing,massive star) neutron captures happen more rapidly than beta decays. Thisis the r-process (for rapid) and it occurs to some extent in core-collapse su-pernovae and perhaps reaches its greatest heights in neutron star-neutron starmergers (as were touched upon in Sec. 5). In this case, the chain of neutroncaptures may continue to quite high atomic mass even given a dearth of pro-tons – i.e., into highly unstable nuclei. But when the neutron flux drops off,it’s closing time: the isotopes can’t go home and they “can’t stay here” – theywill undergo a series of beta decays, moving steadily up and to the left inFig. 43 until a stable isotope is reached.

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19.6. Supernovae Observations and Classification

19.6 Supernovae Observations and Classification

The observation and classification of supernovae go back over 1000 years,making this one of the oldest branches of observational astronoy. The name“nova” had been given to “new stars” (actually outbursts from accreting whitedwarfs), and “super”-novae were that much brighter. The names are similarin other cultures; e.g., Chinese records refer to them as kexing, or “guest stars.”

Before the modern era began, there were ∼8 supernovae visible with-out telescopes. The brightest of these, SN 1006, is estimated to have hadmV ≈ −7.5 mag, roughly 3 mag brighter than Venus and visible even inthe daytime. Another famous example os SN 1054, whose ejecta now span aradius of ≈1.7 pc – this is the famous Crab Nebula3 The two most famous,local (i.e., in the Milky Way) supernovae in “recent” times are Tycho’s andKepler’s supernovae; these occurred “only” 30 years apart, in 1572 and 1604,and in Europe helped break down believes in a static, unchanging heavensand to unleash the modern astronomical revolution. No SN have been seen inthe Milky Way since, although we think there should be 1–3 per year.

Like the classification of stars (discussed in Sec. 8), supernovae were clas-sified into groups first and only later associated with underlying physicalmechanisms. The observationally-motivated nomenclature comes from opticalspectra of the supernova near peak luminosity (when it’s easiest to observe),and it is:

• Type I: No H-α line seen.

• Type II: H-α line seen.

As simple as that! But this was subsequently clarified:

• Type Ia: No H-α, but Si lines seen.

• Type Ib: No H-α, but He lines seen.

• Type Ic: No H-α, and not much else.

• Type II: H-α line seen.

There are also multiple types of Type II supernovae, classified on the basisof their light curve morphology. E.g. SN1987A (lightcurve shown in in therightmost panel of Fig. 41) was classified as Type IIpec, for “peculiar.”

A Type Ia supernova is caused by fusion detonation on a degenerate whitedwarf. Once the main source was thought to be mass transfer from a nearbybinary companion onto the white dwarf, until the WD’s degeneracy pressurecan no longer support itself. But we now know that there are many pathwaysleading to SNe Ia; different pathways lead to different chemical abundancesin the SN ejecta, and these studies now indicate that most SNe Ia (at leastin dwarf galaxies) occur from white dwarfs of roughly ∼ 1M�, well belowthe Chandrasekhar Mass of 1.4M�. These SNe Ia are typically brighter — less

3Note that its ejecta have moved ∼5 light years over the past millenium, implying an averagespeed of 0.5% c – and presumably higher (and more relativistic) at earlier times.

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19. On the Deaths of Massive Stars

total energy is released, but more of the energy here goes into photons ratherthan into neutrino luminosity.

Types II, Ib, and Ic are all different flavors of core-collapse supernovaeprobably resulting from progenitor stars with different initial masses and evo-lutionary histories.

In many supernovae, many of the photons we see actually come from theradioactive decay of unstable isotopes produced in the explosion. The mostimportant pathway comes from the decay of 56Ni, which was itself producedfrom fusion of Si with a succession of α particles:

(484) 2814Si + 74

2He →5628 Ni.

The decay pathway after the supernova is over and nucleosynthesis has ceasedis

56Ni →56 Co + e+ + νe + γ (6.1dayhalf − life)(485)

56Co →56 Fe + e+ + νe + γ (78dayhalf − life)(486)

(487)

Note that the 56Co phase of SN1987A is indicated in Fig. 41. That SN wasestimated to produce just 0.075M� of 56Ni, but others produce as much as∼ 1M� — these are extremely luminous.

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